Dividing image radially
This isn't exactly procedural, but it's OK for a one-off, maybe.

Create a single segment.



Start with a whole 36-section circle, rotated, inset,and translated in Edit Mode as shown, so its origin is at the center of an edge, at World 0. We're working in XY, Z out of the screen.



Select out the bottom segment, V rip the internal edges, and P separate by loose parts into 3 objects. Parent the point to the midsection, and the midsection to the base.



Make hierarchies of left and right segments.

ShiftD duplicate all the parts of the segment in place, and place the origin of the duplicate in its bottom-left corner. In Object Mode, with Snap set to 'Vertex'  Shift D X duplicate it to the right, and snap the duplicate to the original, in one move.

Shift R repeat the move, until you have 18 segments, not counting the original, which you can delete.

Do the same on the left, this time with the origins of the objects at the bottom-right corner, stopping at 17 segments.

Now we have to parent the base of each segment to the next, working towards the center. This is tedious, so you can do it with this little script, having selected the (bases only)  of the right and left-hand groups in two batches, switching the reverse parameter in the script appropriately:

import bpy

obs = bpy.context.selected_objects


# set reverse = True for right (positive X) segments
obx  = sorted (obs, key=lambda ob: ob.location[0], reverse=False)

for i in range(len(obx)-1):
    obx[i].parent = obx[i+1]
    obx[i].matrix_parent_inverse = obx[i+1].matrix_world.inverted()


Now when you set the Pivot to 'Individual Origins' and rotate the bases in Z, a curl results:



.. and R Z10 closes the right half of the circle. This rotation is keyable. On the left, it's R Z-10

When all the segments are present and selected in the curled position, and all thrown into Edit Mode simultaneously, they can be UV mapped together with 'Project from View: Bounds'. Then they can all share the same material, and all acquire their own UV map into the image texture.

Then you're kitted up to animate the rotations, and later the translations of the segment-sections.